Gravitational waves in ultra-slow-roll and their anisotropy at two loops

Abstract

We compute the non-Gaussian corrections to the energy density and anisotropies of gravitational waves induced during the radiation era after an ultra-slow-roll phase of inflation by using a diagrammatic approach, and present the corresponding Feynman rules. Our two-loop calculation includes both the intrinsic non-Gaussianity of the inflaton perturbation δϕ and the non-Gaussianity arising from the nonlinear relation between the latter and the curvature perturbation ℛ, which we find to be subdominant with respect to the former. We apply our formalism to an analytical model in which the ultra-slow-roll phase is followed by a constant-roll stage with a nonvanishing second slow-roll parameter η, and address the renormalization of the one-loop scalar power spectrum in this scenario.